Under Step 5 (Verify that the Apple Mobile Device USB Driver is installed), I found the iPod under “Portable Devices” and followed the steps to update the device driver. The driver is in the “C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers” folder. Once that was done, I restarted iTunes and my iPod was recognized immediately.

After installing iTunes on a fresh install of Windows, the music library was empty! Apple has a support article explaining how to get it back. I had a copy of the XML file and could use it to recreate the Library according to the instructions.